






'''simple docstring'''







import math


def       __UpperCamelCase					(      lowercase_       :  int   ):
       """simple docstring"""




       a_						     =			math.loga(math.sqrt(4 * positive_integer + 1   ) / 2 + 1 / 2   )

       return exponent == int(lowercase_   )


def       __UpperCamelCase					(      lowercase_       :  float = 1 / 12_345   ):
       """simple docstring"""




       a_						     =			0
       a_						     =			0

       a_						     =			3
       while True:
              a_						     =			(integer**2 - 1) / 4
              # if candidate is an integer, then there is a partition for k
              if partition_candidate == int(lowercase_   ):
                     a_						     =			int(lowercase_   )
                     total_partitions += 1
                     if check_partition_perfect(lowercase_   ):
                            perfect_partitions += 1
              if perfect_partitions > 0:
                     if perfect_partitions / total_partitions < max_proportion:
                            return int(lowercase_   )
              integer += 1


if __name__ == "__main__":
  print(f"""{solution() = }""")












'''simple docstring'''







from __future__ import annotations

from collections.abc import Iterator
from typing import Generic, TypeVar

__lowerCAmelCase        =							TypeVar("T")




class   __SCREAMING_SNAKE_CASE       (Generic[T]       ):


  """simple docstring"""


  def __init__(			self   ,	UpperCamelCase__	):






         """simple docstring"""


         a_						     =			data
         a_						     =			None







  def __str__(			self	):






         """simple docstring"""


         return f'{self.data}'





class   __SCREAMING_SNAKE_CASE       (Generic[T]       ):


  """simple docstring"""


  def __init__(			self	):






         """simple docstring"""


         a_						     =			None







  def __iter__(			self	):






         """simple docstring"""


         a_						     =			self.top
         while node:
                yield node.data
                a_						     =			node.next







  def __str__(			self	):






         """simple docstring"""


         return "->".join([str(UpperCamelCase__	) for item in self]	)







  def __len__(			self	):






         """simple docstring"""


         return len(tuple(iter(self	)	)	)







  def    _a       (			self	):






         """simple docstring"""


         return self.top is None







  def    _a       (			self   ,	UpperCamelCase__	):






         """simple docstring"""


         a_						     =			Node(UpperCamelCase__	)
         if not self.is_empty():
                a_						     =			self.top
         a_						     =			node







  def    _a       (			self	):






         """simple docstring"""


         if self.is_empty():
                raise IndexError('pop from empty stack'	)
         assert isinstance(self.top   ,	UpperCamelCase__	)
         a_						     =			self.top
         a_						     =			self.top.next
         return pop_node.data







  def    _a       (			self	):






         """simple docstring"""


         if self.is_empty():
                raise IndexError('peek from empty stack'	)

         assert self.top is not None
         return self.top.data







  def    _a       (			self	):






         """simple docstring"""


         a_						     =			None


if __name__ == "__main__":
  from doctest import testmod

  testmod()




